Asymptotic Theory in Model Diagnostic for General Multivariate Spatial Regression

Table 1

The empirical probabilities of rejection of the KS and CvM tests for several selected values of , , , and . The sample sizes are selected to and . The simulation results are based on 10000 runs.

Sample size
	0	0	0	0	4.90%	1.31299	4.60%	2.52127
	10	0	0	0	10.60%	1.52902	11.28%	4.11538
	20	0	0	0	32.80%	1.71455	33.40%	6.26419
	40	0	0	0	88.64%	1.86015	87.22%	10.37546
	0	50	0	0	5.03%	1.28540	5.33%	2.63926
	0	200	0	0	4.43%	1.22630	5.90%	2.57881
	0	300	0	0	4.60%	1.18783	7.03%	2.52180
	0	500	0	0	4.63%	0.90516	11.00%	2.32439
	0	0	50	0	4.83%	1.27888	5.03%	2.59347
	0	0	100	0	5.17%	1.29476	5.20%	2.68005
	0	0	200	0	6.03%	1.28627	5.23%	2.53931
	0	0	500	0	8.23%	1.27694	7.73%	2.71275
	0	0	0	50	5.00%	1.27241	5.03%	2.69462
	0	0	0	100	4.77%	1.23645	4.63%	2.56912
	0	0	0	300	4.77%	1.27318	5.07%	2.53470
	0	0	0	500	4.97%	1.26322	4.97%	2.55223
	10	50	0	0	11.34%	1.55144	12.22%	3.82300
	10	100	0	0	11.12%	1.49017	12.70%	3.81009
	10	200	0	0	11.20%	1.52118	12.06%	3.71303
	10	500	0	0	12.46%	1.10222	22.44%	2.87591
	20	50	50	50	32.78%	1.76263	33.62%	5.75683
	20	50	100	50	31.80%	1.71323	32.52%	5.98971
	20	50	200	50	28.16%	1.68594	29.16%	5.79669
	20	50	500	50	27.08%	1.52512	28.86%	4.92925
	50	50	50	20	98.60%	1.86506	97.60%	13.43552
	50	50	50	40	98.60%	1.83424	97.95%	13.10968
	50	50	50	60	98.55%	1.91241	98.25%	13.49794
	0	0	0	0	4.75%	1.26388	4.55%	2.52770
	10	0	0	0	11.35%	1.48925	11.40%	3.70839
	20	0	0	0	33.65%	1.75109	33.40%	5.82381
	30	0	0	0	65.70%	1.82802	64.90%	8.31756
	0	50	0	0	4.70%	1.26907	4.95%	2.60854
	0	200	0	0	4.75%	1.23471	5.90%	2.53725
	0	300	0	0	5.35%	1.19808	7.35%	2.62291
	0	0	50	0	0.0485	1.27867	5.15%	2.57206
	0	0	100	0	4.35%	1.23893	4.45%	2.40576
	0	0	200	0	5.80%	1.27524	5.50%	2.62313
	0	0	500	0	8.45%	1.28708	6.50%	2.64556
	0	0	0	50	5.00%	1.28525	4.85%	2.71581
	0	0	0	100	4.50%	1.25700	4.70%	2.57227
	0	0	0	500	4.70%	1.25102	5.10%	2.51076
	20	50	0	0	32.10%	1.70264	32.30%	5.72887
	20	100	0	0	33.55%	1.74878	32.50%	5.76105
	20	200	0	0	33.30%	1.72065	34.35%	5.71531
	20	500	0	0	33.90%	1.61848	46.30%	5.77714
	30	50	100	0	62.55%	1.78912	61.80%	8.08037
	30	50	200	0	60.50%	1.79929	58.60%	7.76765
	30	50	500	0	56.35%	1.78203	54.00%	7.76498
	20	20	20	20	32.55%	1.70930	33.05%	5.60510
	30	50	50	50	63.10%	1.86549	61.65%	8.63149
	50	50	50	50	97.75%	1.88146	97.10%	13.27029
	50	100	50	50	97.60%	1.89668	96.90%	13.30456